A hybrid numerical/analytic technique for the computation of wave fields in stratified media based on the Hankel transform

Abstract

A hybrid numerical/analytic technique is presented for computing the field due to a monochromatic point source in a horizontally stratified medium. It is based on the exact Hankel transform relationship between the field in the range domain and the associated depth‐dependent Green’s function in the horizontal wavenumber domain. The method uses a numerical evaluation of the Hankel transform. It is shown that a major source of error in such an evaluation arises from undersampling of the Green’s function at points where it becomes infinite. This error is described in terms of aliasing, analogous to the aliasing that has been well‐described for the discrete Fourier transform. It is shown that the error can be substantially reduced by removing the infinities, calculating the Hankel transform of the remaining portion of the Green’s function numerically, and adding to it the analytically computed Hankel transform of the infinities. The sum of the analytic terms and the remaining Hankel transform always exactly equals the true field with no errors introduced other than those associated with the numerical evaluation of the Hankel transform, and the method is accurate in both the near‐ and farfield regions. The technique is developed in detail for the acoustics problem of a monochromatic point source and receiver in an isovelocity fluid half‐space overlying a horizontally stratified fluid medium. It is found that under circumstances of interest in ocean bottom acoustics, where the Green’s function has only a few singularities along the real horizontal wavenumber axis, the technique is efficient and extremely accurate.